Journal of Integer Sequences, Vol. 18 (2015), Article 15.7.4

An Aperiodic Subtraction Game of Nim-Dimension Two

Urban Larsson
Department of Mathematics and Statistics
Dalhousie University
6316 Coburg Road
P.O. Box 15000
Halifax, NS B3H 4R2

Nathan Fox
Department of Mathematics
Rutgers University
110 Frelinghuysen Road
Piscataway, NJ 08854


In a recent manuscript, Fox studied infinite subtraction games with a finite (ternary) and aperiodic Sprague-Grundy function. Here we provide an elementary example of a game with the given properties, namely the game given by the subtraction set {F2n+1 - 1}, where Fi is the ith Fibonacci number, and n ranges over the positive integers.

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(Concerned with sequences A000201 A001950 A003623 A026352 A089910 A242082.)

Received April 9 2015; revised versions received July 14 2015; July 15 2015. Published in Journal of Integer Sequences, July 16 2015.

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